How Mathematics Is Rooted in Life
Focusing on the life and contributions of Luitzen Egbertus Jan Brouwer, the book explores his significant role in topology and his complex personality. It delves into his philosophical insights and the controversies surrounding his ideas, presenting a nuanced portrait of a mathematician whose genius shaped modern mathematical thought.
In this new printing, suggestions and comments of readers have been adopted, a number of errors have been corrected, and some definitions have been streamlined. In addition some material (exercises) has been rearranged.
These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature.
This book constitutes the strictly refereed post-workshop proceedings of the 10th International Workshop on Computer Science Logic, CSL'96, held as the 5th Annual Conference of the European Association of Computer Science Logic (EACSL), in Utrecht, The Netherlands, in September 1996. The volume presents 26 revised full papers selected from a total of initially 75 papers submitted; also included are two refereed invited contributions. The volume addresses all current issues in the area of computer science logic research, and is thus a unique record of recent progress in the area.
Der mathematische Intuitionismus, entwickelt von L. E. J. Brouwer, revolutionierte zu Beginn des 20. Jahrhunderts die Grundlagen der Mathematik. Durch seine konstruktive Neubegründung stellte Brouwer die traditionellen Auffassungen in Frage und legte den Fokus auf die Bedeutung der mathematischen Intuition und der Konstruktion von Zahlen. Diese Bewegung beeinflusste nicht nur die Mathematik, sondern auch die Philosophie und die Grundlagenforschung, indem sie neue Perspektiven und Ansätze für mathematische Beweise und Konzepte eröffnete.